How long to melt plastic through composite material?

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To calculate the time required to melt polyethylene plastic through a composite material, one must consider the thermal properties of both the paper and aluminum layers. The equations involved include the heat transfer equation dQ/dt = kTA dT/dx, where k represents thermal conductivity, A is the area, and dT/dx is the temperature gradient. The composite's effective thermal conductivity can be determined using the equation 1/kT = 1/kPaper + 1/kAlu. The power supplied to the system is 1500 W, and the temperature gradient is derived from the difference between the heat source (350 F) and the melting point of the plastic (325 F). Additionally, the heat capacity of the plastic should be factored into the calculations to accurately determine the melting time.
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How could I calculate how much time would be required to melt a plastic through a composite material?

Composite is .005 inches paper and .0003 inches of Aluminum
Plastic is .001 inches polyethlene with melting point of 325 F

Assume heat source is uniform across area of composite
 
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According to the Physics Forums Guidelines (which you agreed to), you have to show how you started this problem.
 
What I've done so far is research and realized my ability of working with differential calculus is lacking. But I do believe that the equations needed are:

dQ/dt = kTA dT/dx

1/kT=1/kPaper +1/ kAlu (so I can figure this out)

A = 2pi 4 inches (1/8 inches)

dQ/dt = the power supplied to the paper side which 1500 W – but I need to solve for dt (not sure how to re-arrange diff calc formula)

dT/dx = (350-73) F to 25 F (So heat source is set at 350 F and the melt point of plastic is 325 F)

I believe I need to consider the heat capacity of the plastic but I’m not sure where – should it be added to the (kT) formula?
 
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